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<H1><A NAME="SECTION03310000000000000000"></A><A NAME="secperf"></A>
<BR>
Factors that Affect Performance
</H1>

<P>
Can we provide <B>portable</B><A NAME="7583"></A> software for computations
in dense linear algebra
that is <B>efficient</B> on a wide range of modern high-performance
computers?
If so, how?
Answering these questions -- and providing
the desired software -- has been the goal of the LAPACK project.

<P>
LINPACK&nbsp;[<A
 HREF="node151.html#dongarra79">38</A>]
and EISPACK&nbsp;[<A
 HREF="node151.html#Smith76">92</A>,<A
 HREF="node151.html#Garbow77">54</A>] have for many years provided
high-quality portable software for linear algebra; but
on modern high-performance computers they often
achieve only a small fraction of the peak performance of the machines.
Therefore, LAPACK has been designed to supersede LINPACK and EISPACK,
principally by achieving much greater efficiency -- but at the same time
also adding extra functionality, using some new or improved algorithms,
and integrating the two sets of algorithms into a single package.

<P>
LAPACK was originally targeted to achieve good performance on
single-processor
vector machines and on shared memory multiprocessor
machines<A NAME="7587"></A> with a modest
number of powerful processors. Since the start of the project,
another class of machines has
emerged for which LAPACK software is equally well-suited--the
high-performance
``super-scalar'' workstations<A NAME="7588"></A>.
(LAPACK is intended to be used across the whole spectrum of modern
computers,
but when considering performance, the emphasis is on machines at the more
powerful end of the spectrum.)

<P>
Here we discuss the main factors that affect the performance of linear
algebra software on these classes of machines.

<P>
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<LI><A NAME="tex2html5015"
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<ADDRESS>
<I>Susan Blackford</I>
<BR><I>1999-10-01</I>
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